The equilibrium volatilities at near infinite dilution of various solutes absorbed in molten polystyrene have been determined by a gas chromatographic technique. This method is much more rapid, although, with the present apparatus, probably less accurate than conventional static techniques. The primary parameters obtained from measurements of retention volumes are the Henry’s law constants, from which are derived the weight and volume fraction activity coefficients, the Flory-Huggins interaction parameters, and the heats of dilution and solution.

Of the solutes investigated, 2-butanone (MEK) was the least, and benzene the most compatible (highest and lowest volume fraction activity coefficients, respectively) with molten polystyrene. A small, but definite, variation of the activity coefficients with polystyrene molecular weight was observed.

INTRODUCTION

This investigation was prompted by the general lack of reported data on the equilibrium vapor pressure of trace amounts of volatiles over molten polymers. The classic technique for obtaining such data involves the use of a microbalance to measure the gain in weight of a polymer sample in a controlled atmosphere of the volatile component. The GC technique is basically a dynamic P-V-T measurement, where the thermodynamic variables may be related to CC parameters such as retention volumes, flow rates, and detector response. Although the former technique is presumably more accurate, the latter was chosen because of its speed and convenience.

The use of polymeric liquid phases in gas-liquid chromatography was firmly established in the late 1950’s in order to provide a stationary phase of limited volatility. Few studies, however, were directly devoted to the study of polymer-solute interactions, perhaps due to the lack of physical and chemical data on these ill-defined macromolecular solvents. Recently, there has been a concerted effort to apply gas chromatography to the physicochemical study of polymer-solvent interactions. These have ranged from the purely analytical studies of Bender and Meloan1 to the assessment of χ parameters by Takamizawa and coworkers.2 In addition to these studies, the recent and extensive work of Guillet et al.3,4 has established the importance of gas-liquid chromatography as a tool in the study of polymers.

At the present time, the technique is confined to the near infinite dilution region (<0.l wt-% solute), where the following assumptions usually apply: (1) the ideal gas law is valid for the vapor phase; (2) absorption equilibrium is rapid; (3) the absorption isotherm is linear. Under these conditions, a basic relationship which may be derived (see Appendix) for reduction of the GC data to a physically meaningful parameter is given by eq. (1) :

Eq. 1. γw = RT / VgP°MS

whereγw is the weight fraction activity coefficient, Vg is specific retention volume, P° denotes vapor pressure of pure solute at temperature T, and MS is the molecular weight of solute. The weight fraction activity coefficient is defined in the usual way, via eq(2):

Eq. 2.p = P°γwW

where p is the partial pressure of solute and W is the weight fraction of solute. This, of course, is a form of Henry’s law for dilute solutions (P°γw being the corresponding Henry’s law constant) using weight fraction as the concentration unit. The use of weight fraction circumvents the intractable question of polymer molecular weight and is simply related to the theoretically more meaningful volume fraction activity coefficient, since:

Eq. 3. γφ/γw = ρs/ρp

where γφ is the volume fraction activity coefficient, and ρs and ρp are the density of solute and density of polymer, respectively, assuming, of course, additivity of volumes on mixing.

The mole fraction activity coefficient has been used by Smidsrød and Guillet,3 employing an equation analogous to eq. (1),

Eq. 4. γχ = RT / VgP°Mn

where γχ is the mole fraction activity coefficient and Mn is the number-average molecular weight of polymer. Although the use of Mn as assumed by the authors is strictly correct (rather than Mw) for the case at hand  a monodisperse polymer as stationary phase  the mole fraction activity coefficient is meaningless in polymer-solvent solution theory.

To illustrate the major advantage of speed and versatility of the GC technique, various model compounds, including alkylated and chlorinated aromatics, and other solutes, were studied. Inspection of the results may give insight into the nature of solute-polymer interactions and perhaps provide a data base which may become useful in the future. The molecular weight of the polystyrenes used was varied to assess properly the effect of that parameter.

EXPERIMENTAL

The polystyrenes employed in this study were obtained from Pressure Chemical Company, Pittsburgh, Pa., and Arro Laboratories, Joliet, Illinois. These particular polymers were of low polydispersity and were polymerized according to the techniques developed by Altares and Wyman.” Additional molecular characterization data have been provided in Table I.

Solutes were obtained from reputable sources and upon chromatography under a multitude of experimental conditions showed no discernible impurities. The support upon which the polystyrene was coated was Chromasorb P, a product of Johns-Manville Corporation, having a mesh range of 80/100. Coating solutions of polystyrene were prepared by dissolving the polystyrene with gentle heating in Baker analyzed reagent grade benzene.

The support has a surface area of about 4m2/g, so that, assuming a uniform coating with polymer, the coating thickness should be at least 0.025 μ. On the other hand, if we assume that the polymer coating doesn’t penetrate at all into the pores of the support, and that the support particles are spherical the maximum coating thickness would be about 5 μ. Presumably, the true average thickness lies between these limits and, if so, should be thin enough to assure equilibrium with solute vapor but thick enough to avoid adsorption effects. After coating was accomplished, the coated support was removed carefully and weighed in a stoppered bottle. The approximate amount of polystyrene deposited on the supports is listed in Table II. At the completion of the experiment, the column contents (Chromasorb and polymer) were removed and submitted for ash analysis. The results of the gravimetric ash analysis (Table II) allowed the computation of the weight of the solvent (liquid phase).

TABLE II. Polystyrene Coating Analysis

Molecular weight (nominal)

3,600

97,200

1,800,000

“Crystal”

Coating, wt/wt-%

15.04

10.53

12.51

15.16

Ash, analysis, %

86.85

90.37

85.34



Weight of polymer on support, g

1.2855

0.9253

1.6142

1.528

aWeight of solvent based on weight of support.bPer cent by weight of initial ash mixture (polymer + support) .

The column was ¼ in. od copper tubing of 1 m length. Glass wool plugs were used to contain the column packing, which was placed into the tube by a gentle tapping procedure. The column ends were capped until actual installation into the gas chromatograph.

Helium was employed as a carrier gas. In order to minimize pressure drop complications in the column, the ratio of inlet to outlet pressure was kept close to unity. A U-tube manometer was filled with mercury and connected to the carrier gas line in front of the injection port for measuring the inlet pressure.

The commercial gas chromatograph employed with the above described modifications was a Microtek GC 2500R, equipped with a thermal conductivity detector. Flow rates were measured with a soap bubble flow meter. Elution profiles were recorded by using a Honeywell Electronik 19 chart recorder.

Oven temperature measurement was accomplished by using a Hewlett-Packard Model HP-2801A quartz thermometer with sampling every 2.4 sec. The two temperature-sensing probes were placed randomly in the oven volume occupied by the column. Room temperature was measured by using a United States Bureau of Standards Certified Thermometer, No. D-12050.

Simple checks on the dependence of solute retention on sample size produced no noticeable variation in retention volume, and the elution profiles were symmetric, which supports the assumption of equilibrium. A Hamilton 10 μl capacity syringe was used for injection of the solutes into the gas flow. Analysis of each solute was done in triplicate by employing 1.0 μl sample sizes.

The reduction of measured retention time to specific retention volume is amply illustrated in several key texts7,8 and will not be discussed here. All saturated vapor pressures were obtained from Dreisbach9 or from internal sources.10

Densities for the solutes were obtained directly from data tabulated in Timmermans’ compilation11 of physicochemical constants. Although the highest temperature used in this study (210° C) was considered to be far enough removed from the lowest critical temperature (263° C for MEK) to justify density extrapolation from data at lower temperatures, the theoretical basis for using densities (rather than partial molar volumes) is insufficient to warrant their use. Therefore, since partial molar volumes are not in general known for the cases at hand, the room temperature (25° C) densities were used in converting weight fraction activity coefficients to volume fraction activity coefficients [eq. (3)]. In any case, the density ratio, as required in eq. (3), should be a less pronounced function of temperature than the densities themselves.

Density data for polystyrene exist in the literature12,13 and are also available as a function of molecular weight.14-16 The value for “crystal” polystyrene was taken as 1.04 g/cc from internal sources.

RESULTS

The pertinent physical and chemical properties of the polystyrenes used are reported in Table I. The analyses of the amount of polymer on the support are tabulated in Table II. Density data and critical temperatures for the various solutes are listed for convenience in Table III.

TABLE III. Solute Propertiesa

Solute

Density (25° C), g/cc

Critical Temperature, ° C

Benzene

0.874

289

Toluene

0.863

320

Ethylbenzene

0.861

344

o-Xylene

0.876

358

m-Xylene

0.860

344

p-Xylene

0.857

343

Styrene

0.906

373

o-Dichlorobenzene

1.303

412

Methyl ethyl ketone

0.800

263

Carbon tetrachloride

1.584

283

p-Dioxane

1.028

315

Chlorobenzene

1.101

359

n-Propylbenzene

0.858

365

aValues taken or extrapolated from the literature.11

The results of the present study on “crystal” polystyrene, in terms of Henry’s law constants, weight and volume fraction activity coefficients, and x parameters, are reported in Table IV. The heats of dilution and solution were calculated from the data of Table IV and are listed in Table V. Weight fraction activity coefficients for the various monodisperse polystyrenes studied are reported in Table VI.

The Henry’s law constant K is simply P°γw, as mentioned in the introduction. The weight fraction activity coefficients were calculated from eq. (1), and volume fraction activity coefficients from eq. (3). The x parameter was calculated by use of eq. (5)

Eq. 5. χ = (ln γΦ) − 1

which was derived from the results of Flory’s theoretical treatment of polymer-solute interactions.l7

The heat of dilution ΔHD (also referred to as the excess heat of solution) was calculated from eq. (6)

Eq. 6. ΔHD = Rd(ln γw)/d(1/T)

and represents the enthalpy change associated with the transference of one mole of pure solute liquid into infinitely dilute solution in the molten polymer.

The heat of solution ΔHS was calculated from:

Eq. 7. ΔHS = Rd(ln K)/d(1/T)

and represents the enthalpy change associated with the transference of one mole of pure solute vapor at one atmosphere into infinitely dilute solution in the molten polymer.

The two enthalpies are simply related to the heat of vaporization, ΔHV, of the soute [sic] by:

Eq. 8. ΔHD − ΔHS = ΔHV

Although the precisions (standard deviations of the slopes of ln γw and ln K vs. 1/T) of these enthalpies (Table V) appear to be of the order of 0.2 kcal/mole or less, the accuracy of the technique is probably no better than 0.5 kcal/mole, as judged from consideration of the various factors which enter into the experimental parameters and the reproducibility of the individual measurements, particularly with respect to column-to-column variations.

DISCUSSION

The results for styrene (Tables IV-VI) can be fairly clearly interpreted, at least qualitatively. The weight fraction activity coefficients are not strong functions of temperature, and therefore give a small value for the heat of dilution. This is not surprising since no great differences would be expected to exist in interactions between styrene molecules in an environment of pure styrene and styrene molecules in an environment of polystyrene.

There is also a shallow but definite dependence on molecular weight, as is to be expected since the solute molecule “sees” only a short segment of the polymer molecule. The effect is similar to that observed for poly(ethylene glycols)18 where Vg changes by ~15% in going from 1000 to 20,000 in molecular weight, and the major change occurs in the low molecular weight region.

Unfortunately, the accuracy of the activity coefficients obtained by the GC method cannot be assessed directly since the appropriate data for polystyrene are not available from literature sources. Data by Kargin19 for hydrocarbon sorption on glassy polystyrene shows limiting slopes of the isotherms which agree qualitatively with the increase in γw with temperature. Our precision is about 3%, and we believe the accuracy should be not more than perhaps 5%.

One direct comparison was found in the literature. Use of an extrapolated value for x1 of 0.26 from Bawn et al.20 for toluene in polystyrene results in a value of 3.56 for γΦ. Our data for toluene at 123° C (γw = 4.52 for polystyrene of 96,000 MW) combined with density data (0.906 g/c for styrene, 1.04 g/cc for polystyrene) give a value of 3.76 for γΦ, a surprisingly close agreement considering the crudeness of the theory.

Inspection of the data for the various solutes over “crystal” polystyrene (Table IV) reveals that methyl ethyl ketone has the largest volume fraction activity coefficient, i.e., is at least compatible with the polystyrene environment, probably due to its being the most polar solute employed. Benzene, on the other hand, has the lowest volume fraction activity coefficient, i.e., is the most compatible with molten polystyrenes, which may be due to favorable π-interactions, and also possibly due to its small molecular size, enabling it to fit into the polymer matrix the most easily.

It should be noted that calculation of partial pressures of styrene and other solutes included in this study, over molten polystyrene, by use of the Henry’s law equation, for example, is valid only to the extent that the absorption isotherm in [sic] linear up to the region of interest. The GC technique and theory, as employed at present are strictly valid only in the near infinite dilution region, which we estimate to be less than about 0.1, wt-%, typical for normal chromatographic conditions, and therefore extrapolation beyond this range should be subject to caution. Some confidence in the assumption of isotherm linearity can be provided by visual inspection of the chromatograms, which appear symmetrical over the range of solute amounts covered in this report. Isotherm nonlinearity has been observed21 even at low concentrations for polar solutes over hydrophobic macromolecules. Additional evidence for isotherm nonlinearity in solute-polymer absorption at the concentration extremes may be seen in the data of Jenckel.22 Isotherm nonlinearity usually manifests itself in peak skewness, proper analysis of which can lead directly to the sorption isotherm.

APPENDIX

The mole fraction activity coefficient at infinite dilution for the solute is given by the standard expression:8

Eq. 9. γχ∞ = RT/VgP°MP

Since the activity coefficients are defined by the expressions (10)

Eq. 10.

the activity coefficients are interconverted by eq. (11).

Eq. 11. γx = γwWS / ΧS

At near infinite dilution, the weight and mole fractions of solute may be expressed as: